Abstract: Dehn surgery is the operation of cutting a solid torus out of the three-sphere and regluing by a twist. The Cosmetic Surgery Conjecture predicts that if this solid torus is knotted then regluing by different twists gives back different three-manifolds. We will give some new partial results towards this conjecture using techniques from gauge theory. No prior familiarity with gauge theory is necessary for the talk. This is joint work with Mike Miller Eismeier.
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